# Hoffman Criterion

The resulting failure index in Hoffman’s theory for an orthotropic lamina in a general state of plane stress (2D) with unequal tensile and compressive strengths is given by:

${F}_{index}=\left(\frac{1}{{X}_{T}}-\frac{1}{{X}_{C}}\right){\text{\sigma}}_{1}+\left(\frac{1}{{Y}_{T}}-\frac{1}{{Y}_{C}}\right){\text{\sigma}}_{2}+\frac{{\text{\sigma}}_{1}^{2}}{{X}_{T}{X}_{C}}+\frac{{\text{\sigma}}_{2}^{2}}{{Y}_{T}{Y}_{C}}-\frac{{\text{\sigma}}_{1}{\text{\sigma}}_{2}}{{X}_{T}{X}_{C}}+\frac{{\text{\tau}}_{12}^{2}}{{S}^{2}}$

- $Xt,Xc$ are the maximum allowable stresses in the 1-direction in tension and compression,
- $Yt,Yc$ are the maximum allowable stresses in the 2-direction in tension and compression,
- $S$ is the allowable in-plane shear stress

## Syntax

`HoffmanFT(tensor,xt,xc,yt,yc,s,sets,plies,elems,parts,props,pool_name,layer_index,opt_str)`

## Arguments

`tensor`- Stress table
`xt`- Allowable tensile stress in ply material direction 1
`xc`- Allowable compressive stress in ply material direction 1
`yt`- Allowable tensile stress in ply material direction 2
`yc`- Allowable compressive stress in ply material direction 2
`s`- Allowable in-plane shear stress
`sets`- Set table (D=NULL)
`plies`- Ply table (D=NULL)
`elems`- Element table (D)
`parts`- Part table (D)
`props`- Property table (D)
`pool_name`- Pool name (D=@current_pool)
`layer_index`- Layer index (D=@current_slice_index)
`opt_str`- This is an optional argument, which can passed if needed (D=option).